The LISE package: Solvers for static and time-dependent superfluid local density approximation equations in three dimensions

Nuclear implementation of the density functional theory (DFT) is at present the only microscopic framework applicable to the whole nuclear landscape. The extension of DFT to superfluid systems in the spirit of the Kohn-Sham approach, the superfluid local density approximation (SLDA) and its extension to time-dependent situations, time-dependent superfluid local density approximation (TDSLDA), have been extensively used to describe various static and dynamical problems in nuclear physics, neutron star crust, and cold atom systems. In this paper, we present the codes that solve the static and time-dependent SLDA equations in three-dimensional coordinate space without any symmetry restriction. These codes are fully parallelized with the message passing interface (MPI) library and the time-dependent code takes advantage of graphic processing units (GPU) for accelerating execution. The dynamic code has checkpoint/restart capabilities and for initial conditions one can use any generalized Slater determinant type of wave function. By generating the appropriate initial quasi-particle wave-functions in a static calculation only, the time-dependent code can describe a large number of physical problems: nuclear fission, collisions of heavy ions, the interaction of quantized vortices with nuclei in the nuclear star crust, excitation of superfluid fermion systems by time dependent external fields, quantum shock waves, domain wall generation and propagation, the dynamics of the Anderson-Bogoliubov-Higgs mode, dynamics of fragmented condensates, vortex rings dynamics, generation and dynamics of quantized vortices, their crossing and recombinations and the incipient phases of quantum turbulence.

密度泛函理论（Density Functional Theory, DFT）的核物理应用，是目前唯一适用于全核物理体系的微观理论框架。以科恩-沙姆方法（Kohn-Sham approach）为思路将DFT推广至超流体系后，衍生出超流体局域密度近似（Superfluid Local Density Approximation, SLDA）；进一步将其拓展至含时场景，得到含时超流体局域密度近似（Time-dependent Superfluid Local Density Approximation, TDSLDA）。上述方法已被广泛用于描述核物理、中子星地壳以及冷原子系统中的各类静态与动力学问题。本文提供了可在三维坐标空间中求解静态及含时SLDA方程的代码，且无任何对称性限制。该套代码完全基于消息传递接口（Message Passing Interface, MPI）库实现并行加速，其中含时代码还可借助图形处理器（Graphic Processing Units, GPU）进一步提升运行效率。动力学代码具备检查点/重启功能，且初始条件可采用任意广义斯莱特行列式（generalized Slater determinant）类型的波函数。仅需通过静态计算生成合适的初始准粒子波函数，含时代码即可用于解决大量物理问题：包括核裂变、重离子碰撞、核星地壳中量子涡旋与原子核的相互作用、含时外场激发超流费米子系统、量子冲击波、畴壁的产生与传播、安德森-博戈留博夫-希格斯模式的动力学、碎裂凝聚体的动力学、涡旋环动力学、量子涡旋的产生与动力学演化、涡旋的交叉与重联，以及量子湍流的初始形成阶段。